Question

If $A$ and $B$ are two disjoint sets, then $(A\cup B^{\prime }{)}^{\prime }\cap (A^{\prime }\cup B{)}^{\prime }$ is

• A. Null set
• B. Universal set
• C. $A^{\prime }$
• D. $B^{\prime }$

Answer 1

The correct option is A Null set

Consider ${(A\cup B^{\prime })}^{\prime }\cap {(A^{\prime }\cup B)}^{\prime }$
$=(A^{\prime }\cap B)\cap (A\cap B^{\prime })$
$=B\cap A$ $=\varphi$ ....Since A and B are disjoint sets